What is the limit as x approaches 0 of ((1-x)^4-1)/x ?

The limit as x approaches 0 of ((1-x)^4-1)/x is -4

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limit as x approaches 0 of ((1-x)^4-1)/x

x \to 0 lim (\frac{( 1 - x ) ^{4} - 1}{x})

- 4

Solution steps

x \to 0 lim (\frac{( 1 - x ) ^{4} - 1}{x})

Simplify

\frac{( 1 - x ) ^{4} - 1}{x} : - (x^{2} - 2 x + 2) (- x + 2)

= x \to 0 lim (- (x^{2} - 2 x + 2) (- x + 2))

Plug in the value

x = 0

= - (0^{2} - 2 \cdot 0 + 2) (- 0 + 2)

Simplify

- (0^{2} - 2 \cdot 0 + 2) (- 0 + 2) : - 4

= - 4

x \to - 4 - lim (x)

x \to 0 lim (\frac{x + x ^{2}}{x ^{2}})

x \to 0 + lim ((sin (x))^{2})

x \to 72 lim (ln (x))

x \to - 3 lim (2 x^{2} - 3)

What is the limit as x approaches 0 of ((1-x)^4-1)/x ?
The limit as x approaches 0 of ((1-x)^4-1)/x is -4